I know that f is 0 at [tex]z=0[/tex], but what is the order of this zero? Is there such a thing as a fractional order zero? Conversely, I know that there is a singularity at [tex]z=\infty[/tex], but this singularity seems to be a fractional order pole. Is this the case? I know that both of these points are also branch points, does that influence the problem at all?